323367960-Updating-ASCE-Manual-No-74.pdf

Electrical Transmission and Substation Structures 2015

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Updating ASCE Manual No. 74: Guidelines for Electrical Transmission Line Structural Loading 1

T. G. Mara and R. H. Behncke

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. d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 6 1 / 8 0 / 9 0 n o s e d n A s o l e d d a d i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D

Ph.D., P.Eng., M.ASCE, The Boundary Layer Wind Tunnel Laboratory, University of Western Ontario, London, ON, Canada N6A 5B9. E-mail: [email protected]

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Ph.D., POWER Engineers, Inc., 2041 South Cobalt Point Way, Meridian, Idaho. E-mail: [email protected]

Abstract

Following the last ASCE Electrical Transmission and Substation Conference (Columbus, OH in 2012), the current roster of the Task Committee on Electrical Transmission Line Structural Loading was assembled to work towards updating ASCE Manual of Practice No. 74: Guidelines for Electrical Transmission Line Structural Loading (ASCE-74). ASCE-74 is currently in its 3 rd Edition, published in 2010, and provides guidance on loading criteria, weather-related loads (i.e., wind and ice), additional load considerations for transmission structures and wires (e.g., longitudinal loads), and an example design considering all relevant load cases. As well, an extensive set of appendices contains useful information relevant to the design and analysis of transmission lines. The 4 th Edition of ASCE-74 is scheduled to be published in 2016, and will contain a number of revisions to the previous edition. Many of these revisions are relevant to weather-related loading (Chapter 2), which is currently the largest section of the Manual. This paper, written on behalf of the ASCE Task Committee on Electrical Transmission Line Structural Loading, outlines significant changes to the weather-related loading (Chapter 2) made for the upcoming edition of the Manual and discusses the reasoning behind some of the revisions. INTRODUCTION

The design of a transmission structure is most often driven by environmental loads such as wind and ice. The underlying methodology of wind loading formulae in many design standards and codes tends to be very similar, although the use of different nomenclature, combination of parameters, and unit conversion tends to complicate a direct comparison among design values arrived at by various documents. ASCE Manual of Practice No. 74: Guidelines for Electrical Transmission Line Structural Loading has historically adopted the wind nomenclature and parameters from ASCE 7: Minimum Minimum Design Loads for for Buildings and Other Other Structures. This paper describes the updates and revisions relevant Chapter 2: Weather-related Loads of the upcoming edition of ASCE Manual of Practice No. 74: Guidelines for Electrical Transmission Line Structural Loading. The major points addressed in the paper involve the following: • • • •

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Wind speed maps Force coefficient Yawed wind on towers Gust response factor


The section related to each of the major points has been written to provide a background on the current method, describe the updated and revised methods, and summarize the implications on design values. It is the hope of the authors that readers will find this paper useful for understanding and applying the updated methods in their use of Manual No. 74. . d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 6 1 / 8 0 / 9 0 n o s e d n A s o l e d d a d i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D

WIND SPEED MAPS ASCE 7 and ASCE-74

In the United States, the reference wind speed is a 3-second gust speed at 33 ft (10 m) height above ground in open country terrain (Exposure Category C) as defined by ASCE 7 and ASCE74. The wind loading criteria in ASCE-74 have traditionally followed the basic wind speed map nd provided in ASCE 7, which resulted in fastest mile wind speeds (33 ft, Exposure C) in the 2 Edition of ASCE-74 (ASCE 1991) and 3-second gust wind speeds (33 ft, Exposure C) in the 3 rd Edition of ASCE-74 (ASCE 2010a). Fastest mile and 3-second gust wind speeds reflect different averaging times, and thus have different values associated with the same mean recurrence interval (MRI), or return period. As the duration of averaging time becomes smaller, the associated magnitude becomes larger. For example, a fastest mile wind speed of 85 mph is equivalent to a 3-second gust wind speed of approximately 100 mph. ASCE 7 adopted the 3second gust wind speed as of ASCE 7-95 (ASCE 1996). In versions of ASCE 7 preceding ASCE 7-10 (ASCE 2010b), a single map of basic wind speeds has been provided for the United States. However, a change in design philosophy has prompted the partial load factor for wind to be incorporated into the wind speed maps used for ultimate strength design beginning with ASCE 7-10. This has led to wind speed maps with MRIs of 300, 700, and 1700 years being included in the main body of ASCE 7, and wind speed maps with MRIs of 10, 25, 50, and 100 being included in the Commentary. Note that the MRIs of 300, 700 and 1700 reflect factored ultimate wind speeds, while the MRIs in the Commentary are not factored. This approach provides a consistent level of risk not achieved in previous versions of ASCE 7, and is advantageous for the design of occupied structures. However, this design philosophy is inconsistent with current procedures and past practice for transmission lines, where load factors often depend on many additional considerations. The wind speed map in the current edition of ASCE-74 (based on ASCE 7-05) has often been thought of as being associated with a 50 year MRI. While this is true for non-hurricane regions (i.e., inside the innermost coastal wind speed contour), it is only partially true for regions affected by hurricanes. In the development of the ASCE 7-05 basic wind speed map, a nominal MRI of 500 years was selected as an ultimate event, the associated wind speeds (containing contributions of non-hurricane and hurricane events) were calculated, and the entire map was reduced by a factor. This factor was associated with the wind speed-return period relationship developed for non-hurricane winds (Peterka and Shahid 1998). However, the slope of this relationship in hurricane regions varies both spatially (along the coast) and in magnitude compared to that for non-hurricane winds. This resulted in the ASCE 7-05 wind speed map being representative of a 50-year MRI in non-hurricane regions and MRIs ranging from approximately 50 to 90 years in hurricane regions (see Chapter C6 Wind Loads in ASCE 7-05 for more

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rd

information). As a result, the current (3 Edition) of ASCE-74 has a single basic wind speed map to be used for design, along with a table of factors to adjust wind loads to other MRIs (return periods) of interest. Updated Wind Speed Maps . d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 6 1 / 8 0 / 9 0 n o s e d n A s o l e d d a d i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D

The wind speed maps in ASCE 7-10 are based on the combination of observed non-hurricane winds (Peterka and Shahid 1998) and simulated hurricane winds (Vickery et al. 2010). Since the analysis by Peterka and Shahid (1998) was carried out, many additional years of wind records have been obtained throughout the United States. Over the past few years, a team at the National Institute of Standards and Technology (NIST) has been developing a new set of wind speed maps based on these more recent records for non-hurricane regions combined with the most recent techniques in hurricane simulation (i.e., Lombardo et al. 2015). The results from this analysis will comprise the design wind speed maps in the upcoming edition of ASCE 7, and will contain wind speed maps for MRIs of 10, 25, 50, 100, 300, 700, 1700 and 3000. Note that MRIs of 300 to 3000 correspond to ultimate wind loads for strength design. As additional wind data was available for the NIST analysis, the wind speed maps provide more resolution in terms of wind speeds than the previous maps used in ASCE 7. The continental United States is now characterized by contours rather than its previous uniform appearance. The hurricane regions remain very similar to those appearing in previous editions of ASCE 7 (and ASCE-74) for comparable MRIs. All data has undergone automatic and manual quality control, as well as having been corrected for issues such as anemometer siting. Additional information on the analysis can be found in Lombardo et al. (2015). After discussion among the Task Committee on Electrical Transmission Line Structural Loading, it has been decided that the upcoming edition of ASCE-74 will likely recommend the 100-year MRI wind speed map as the basis of design. The reasoning for the recommendation of the 100year MRI is important due to the bi-modal characteristics of the wind speed-return period relationship in hurricane regions, as well as maintaining a consistent level of risk for design of transmission lines throughout the United States. For many hurricane regions, the wind speedreturn period relationship is markedly steeper than that for non-hurricane regions. The use of a greater MRI is therefore prudent. Note that in many cases, the wind speeds appearing on the updated 100-year MRI map are of similar magnitude to those provided in the current edition of ASCE-74, although the wind speed values now reflect a consistent MRI of 100 years. The use of the 100-year MRI maps will result in a +/- 5 mph difference in design wind speed for most nonhurricane regions compared to the current design wind speed map in ASCE-74. However, the use of factors to move to other MRIs of interest is not an accurate way of working with the new maps; options are currently being explored to include wind speed maps for other (higher) MRIs in the upcoming version of ASCE-74. Wind speed maps associated with greater MRIs (e.g., 200year, 300-year) may be of interest to some designers, and will be available for reference in an appendix of the upcoming edition of ASCE-74. Additional ice maps corresponding to these MRI will also be available for reference in the same appendix. In summary, the wind speed maps provided in the upcoming edition of ASCE-74 offer distinct advantages to the single map provided in the current edition:

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1) Updated analysis based on additional years of wind speed observation. 2) Risk-consistent approach for hurricane and non-hurricane regions. 3) The opportunity to design to a greater MRI if desired, and to do so in a more accurate manner than previously available.


4) The MRIs of the wind speed maps will be consistent with the MRIs of the maps for extreme ice. FORCE COEFFICIENT



The force coefficient, , accounts for the effects of member characteristics (e.g., shape, size, solidity) on the resulting wind load. It is also commonly referred to as the drag coefficient, pressure coefficient, or shape factor. The primary parameter which influences the force coefficient for lattice truss structures is the solidity ratio. The solidity ratio, , is typically calculated for each face of the structure as

Φ

Φ = 

 

where is the area of all members in the windward face of the structure (also referred to as the net area) and is the area of the outline of the windward face of the structure (also referred to as the gross area). The solidity ratio should be calculated for a number of panels along the height of a tower, as the solidity of the design often varies for different sections of the tower. Force coefficients for normal wind on lattice truss structures having flat-sided members are provided for square and triangular truss structures in ASCE 7 (ASCE 2010b). These values are shown in Table 1. A correction factor may also be applied to the force coefficient to accommodate sections with rounded members, as shown in (Eq. 1). Note that these values differ slightly from those in the previous version of ASCE-74, which were based on the ASCE 7-88 (ASCE 1990). ASCE 7 discontinued the use of the discrete force coefficient expressions as of ASCE 7-95 in favor of the continuous force coefficients in Table 1, which are also consistent with those specified in ANSI/TIA (2005). The force coefficients in Table 1 are compared with those used in previous editions of ASCE-74 in Figure 1. Note that the updated force coefficients result in lower values for sections with solidity lower than approximately 30%. Table 1. Force coefficients (

 

) for normal wind on lattice truss structures having flat-sided members (after ASCE 7-10b).

Tower Cross Section Square Triangular 2

Correction factor = 0.51 Φ + 0.57

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

4.0Φ - 5.9Φ + 4.0 3.4Φ2 - 4.7Φ + 3.4 where Correction factor < 1.0

(Eq. 1)


158

4.5

Square Cross-section

4.0

Flat-sided (ASCE 7-10) Rounded (ASCE 7-10) Flat-sided (ASCE 7-88) Rounded (ASCE 7-88)

f

C 3.5

, t n e i c i f f e o C e c r o F


3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Solidity Ratio, Φ

a) 4.5 4.0

Triangular Cross-section

Flat-sided (ASCE 7-10) Rounded (ASCE 7-10) Flat-sided (ASCE 7-88) Rounded (ASCE 7-88)

f

C 3.5

, t n e i c i f f e o C e c r o F

3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0

b)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Solidity Ratio, Φ

Figure 1. Comparison of force coefficients for a) square truss structures and b) triangular truss structures.

In summary, the force coefficients have been updated to be consistent with those used in ASCE 7 and ANSI/TIA 222. Items to note about the updated force coefficients are: 1) Continuous equations (as a function of solidity) rather than discrete. 2) Typical trusses with flat-sided and rounded members will have slightly lower force coefficients (for solidity ~ 25%). 3) Compact sections characterized by a high solidity (i.e., 35% to 60%) will have slightly higher force coefficients than recommended in the previous version of ASCE-74.

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YAWED WIND ON TOWERS

The wind load accumulated by a 3-dimensional truss is challenging to assess due to the shielding caused by members in the windward face and complex geometries that can exist in lattice trusses. The approach to the loading on lattice towers under yawed wind was revisited during the preparation of the upcoming edition of ASCE-74, considering new wind tunnel data available for lattice towers. As given by ASCE-74 (ASCE 2010a), the basic equation for wind force acting on the surface of a transmission line or components can be determined by


 =      

(Eq. 2)

For latticed truss structures under yawed wind, the following equations are also provided which calculate the wind force in the transverse and longitudinal directions directly as

 =        cosΨ

(Eq. 3)

 =        sinΨ

(Eq. 4)

following the sign convention in Figure 2, where Ψ is the yaw angle of the wind with respect to the transverse direction (i.e., 0° is the transverse direction, 90° is the longitudinal direction). The remainder of the variables are defined in ASCE-74.

Figure 2. Sign convention for yawed wind on a transmission line (ASCE 2010a).

Relatively few experiments aimed at assessing the wind load on lattice sections have been carried out in the wind tunnel, mainly due to the challenges posed by testing at reduced scales. Bayar (1986) examined yawed winds on a square (in plan) lattice frame which was based on the tower portion of a transmission tower. It was shown that slight increases did exist for yawed wind directions, although the increases were relatively small in magnitude. However, the model was square in plan view, and thus the aspect ratio of each face is fairly similar. This results in the drag load at yawed wind directions to be relatively consistent with that on each of the faces (i.e., at 0° and 90°). Wind tunnel tests on models of square sections (BEAIRA 1935, Bayar 1986) and a cross-arm section (Mara et al. 2010) have demonstrated that the maximum effective wind loads occur for yawed winds ranging from 30° to 45°.

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An equation similar to that currently used in the International Electrotechnical Commission Standard 60826:2003 (IEC 2003) is recommended to account for yawed wind on lattice structures. This is shown in (Eq. 5).

 =     1 + 0.2sin 2Ψ  cos  Ψ +   sin  Ψ . d e v r e s e r s t h g i r l l a ; y l n o e s u l a n o s r e p r o F . E C S A t h g i r y p o C . 6 1 / 8 0 / 9 0 n o s e d n A s o l e d d a d i s r e v i n U y b g r o . y r a r b i l e c s a m o r f d e d a o l n w o D

(Eq. 5)

The experimental transverse drag loads on a typical tower cross-arm are plotted against ASCE74 (ASCE 2010a) and IEC (IEC 2003) calculated drag loads in Figure 3. It is shown that the IEC equation better captures the increase in drag on the cross-arm section, where the ASCE-74 value is a maximum at 0° and decreases with the wind vector. Further description of the wind tunnel tests and comparisons are available in Mara and Ho (2011) and Mara and Behncke (2015). 8

Transverse Effective Drag

6

) m (

2

p

A d C

4

2 ASCE-74 IEC-2003 Experimental 0 0°

10°

20°

30°

40°

50°

60°

70°

80°

90°

Yaw Angle 50

Full tower effective drag

40

) 30 m (

2

p

A d C 20 ASCE-74 - Net ASCE-74 - Transverse ASCE-74 - Longitudinal IEC-2003 - Net IEC-2003 - Transverse IEC-2003 - Longitudinal

10

0 0°

10°

20°

30°

40°

50°

60°

70°

80°

90°

Yaw Angle

Figure 3. Comparison of experimental and calculated transverse drag load on cross-arm only and full tower.

© ASCE


Based on the examination of the behavior of tower portions which have different aspect ratios, the Task Committee agreed that it would be prudent to re-instate the IEC equation for yawed wind on structures. It is acknowledged that this method differs from that recommended in the current edition of ASCE-74 (ASCE 2010a). While little difference exists between (Eq. 5) and the current method for trusses which are symmetric in plan view (i.e., square section), the aerodynamics of portions of the structure which are not symmetric in plan view (i.e., cross-arm or bridge) are much better captured using (Eq. 5).


In summary, the orthogonal approach to the calculation of wind loads in the transverse and longitudinal directions has been shown to underestimate the transverse force for some truss geometries (i.e., geometries with very different transverse and longitudinal faces and properties). As a result, the yawed wind load on the structure should be calculated using (Eq. 5), then decomposed in the transverse and longitudinal loads. By doing so, the differences in the faces are properly augmented based on the yawed wind direction. While there is some difference in magnitude of the experimental and theoretical drag force for the example cross-arm, this difference likely varies among geometries. For some sections, the drag loads on the tower may be greater for low yawed wind directions, and the overall tower-line load may exceed that for the transverse direction. Additional discussion and comparisons are provided in Mara and Behncke (2015). GUST RESPONSE FACTOR

The gust response factor (GRF) accounts for load effects due to the turbulence characteristics of the wind and the dynamic amplification of the structure and wires. That is, depending on the characteristics of a structure (i.e., height, span, frequency, damping), different towers may respond differently to similar wind loading conditions. The equations for the GRFs in previous versions of ASCE-74 are based on the work by Davenport (1979) and have been used by numerous parties in the design of transmission lines for wind loading. However, the original GRF equations were constructed to estimate a peak response from an average (or sustained) wind speed. When ASCE Standard 7 (Minimum design loads for buildings and other structures) adopted a 3-second gust wind speed as the averaging time for design wind speed (as of ASCE 795), the existing GRF equations were no longer compatible. This discrepancy has been reconciled for the upcoming edition of ASCE-74, and is explained in greater detail in Mara (2015). Similarly to previous versions of ASCE-74, two methods for the calculation of the GRFs are provided: a simplified method and a complete method. The simplified method is recommended in Chapter 2 of ASCE-74, and does not consider the effects of resonance. For transmission structures of typical height and span, the assumption that the structure exhibits relatively rigid behavior under fluctuating wind is likely adequate. Therefore, the total dynamic response of the tower is likely well approximated by the background component of the dynamic response only (no resonance). The complete GRFs are described in detail in Mara (2015).

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The simplified GRFs for the structure and wires are expressed as

 = 1+1 +6.4.61   = 1+1+4.6.61


(Eq. 6)

(Eq. 7)

where the background component of the dynamic response for the structure and wire, respectively are as in previous editions of ASCE-74.

 =  1+ 0.156   =  1+ 10.8

  and

,

(Eq. 8)

(Eq. 9)

A notable difference between the updated method and the previous method is the direct calculation of a level of turbulence intensity, or gustiness, of the wind. The turbulence intensity is denoted by , and varies with exposure category and effective height, as shown in (Eq. 10).



  33  =      



(Eq. 10)

is the turbulence intensity at any height , and scales the magnitude of the turbulence intensity depending on Exposure Category. Values of for Exposure Categories B, C and D are provided in ASCE-74 (and shown in Table 2). This approach replaces the previous methodology in which a surface drag coefficient, , was assumed and used to calculate an exposure factor, . The intent of the exposure factor was to provide a level of fluctuating wind depending on the upstream terrain. This change reflects an updated approach to turbulence intensity in the atmospheric boundary layer and is consistent with the wind loading provisions in ASCE 7. The variables and are therefore no longer used in the calculation of the GRFs. The updated table of wind parameters is shown in Table 2.



 









Table 2. Wind parameters by Exposure Category.

Exposure B C D

© ASCE

7.0 9.5 11.5

4 6.5 9

0.3 0.2 0.15

(ft) 170 220 250



(ft) 1200 900 700


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A comparison of the wind pressure calculations over a range of heights are shown in Figure 4 for i) the current ASCE-74 GRF (ASCE 2010a), ii) the updated GRF, and iii) a mean-based approach based on a mean wind speed and unmodified GRF. 25 20 ) f s p ( e r 15 u s s e r P 10 d n i W 5


Wind Pressure on Structure Exposure Category B

Updated GRF ASCE-74 (2010a) Mean-based

0 40

60

80

100

120

140

160

180

200

Total Structure Height (ft) 30 25 ) f s p ( e r 20 u s s e r P 15 d n i W10

Wind Pressure on Structure Exposure Category C


5 40

60

80

100

120

140

160

180

200

Total Structure Height (ft) 35 30 ) f s p ( e r 25 u s s e r P 20 d n i W15

Wind Pressure on Structure Exposure Category D


10 40

60

80

100

120

140

160

180

200

Total Structure Height (ft)

Figure 4. Wind pressure on structure based on different GRF methods.

© ASCE


It is shown that for Exposure C each of the methods result in similar values, with the current ASCE-74 GRF resulting in slightly higher wind pressures at lower heights (less than 80 ft). The updated method predicts lower values for Exposure B and in the current version of ASCE-74, while it results in higher values for Exposure D. These exposures are more sensitive to difference in power law coefficient (which describes the increase in wind speed with height) than Exposure C, although they tend to be used less frequently in practice. The plots in Figure 4 do not consider the effects of resonance, and are based on the simplified method for the GRF as described in Mara (2015). The simplified method is considered adequate for structures of typical height and span length, and GRFs corresponding with this approach have appeared in Chapter 2 of previous editions of ASCE-74 (ASCE 1991, 2010a).


In summary, the gust response factors have been updated to be compatible with a 3-second gust wind speed rather than a sustained wind of longer duration. Key points to note about the updated gust response factors are: 1) The resulting wind pressure for Exposure C among all methods is very similar, with only a 3% difference (reduction) for a typical 100 ft structure. 2) Greater wind pressures result for structures and wires in regions characterized by Exposure D than in the current edition of ASCE-74. 3) Lower wind pressures result for structures and wires in regions characterized by Exposure B than in the current edition of ASCE-74. CONCLUSIONS

This paper described the updates and revisions relevant to Chapter 2: Weather-related Loads of the upcoming edition of ASCE Manual of Practice No. 74: Guidelines for Electrical Transmission Line Structural Loading. The major points addressed in the paper involve the following: • • • •

Wind speed maps Force coefficient Yawed wind on towers Gust response factor

While this paper only addressed revisions to Chapter 2 of ASCE-74, there have been many other revisions and expansions made to the remaining chapters of ASCE-74 as well. Readers and users of ASCE-74 are invited to explore the entire upcoming edition of ASCE-74 for useful information regarding the design and analysis of transmission structures. ACKNOWLEDGEMENTS

The authors acknowledge the contributions of the members of the Task Committee on Electrical Transmission Line Structural Loading.

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REFERENCES

American Society of Civil Engineers (ASCE). (1990). Minimum design loads for buildings and other structures (Revision of ANSI A58.1-1982). ASCE Standard 7-88, ASCE, New York, NY. nd ASCE. (1991). Guidelines for Electrical Transmission Line Structural Loading (2 Edition). ASCE Manuals and Reports on Engineering Practice No. 74, ASCE, New York, NY. ASCE. (1994). Minimum design loads for buildings and other structures. ANSI/ASCE Standard 7-93, ASCE, New York, NY. ASCE. (1996). Minimum design loads for buildings and other structures. ANSI/ASCE Standard 7-95, ASCE, New York, NY. ASCE. (2002). Dynamic Response of Lattice Towers and Guyed Masts. Ed. M.K.S. Madugula, ASCE, Reston, VA. ASCE. (2006). Minimum design loads for buildings and other structures. ASCE/SEI Standard 705, ASCE, Reston, VA. ASCE. (2010a). Guidelines for Electrical Transmission Line Structural Loading (3 rd Edition). ASCE Manuals and Reports on Engineering Practice No. 74, ASCE, Reston, VA. ASCE. (2010b). Minimum design loads for buildings and other structures. ASCE/SEI Standard 7-10, ASCE, Reston, VA. Bayar, D.C. (1986). “Drag coefficients of latticed towers.” J. Struct. Eng., 112(2), 417-430. British Electrical and Allied Industries Research Association (BEAIRA) (1935). “Wind pressure on latticed towers – tests on models.” Report (F/T 84) of the British Electrical and Allied Industries Research Association, Journal of the Institution of Electrical Engineers , 77, 189-196. Davenport, A.G. (1979). “Gust response factors for transmission line loading.” Proc. 5th Int. Conf. on Wind Eng., IAWE, Fort Collins, CO. International Electrotechnical Commission (IEC). (2003). “Loading and strength of overhead transmission lines.” International Standard IEC 60826, 3 rd Ed., International Organization for Standardization, Technical Committee 11, Geneva, Switzerland. Lombardo, F., Pintar, A., Vickery, P.J., Simiu, E., and Levitan, M. (2015). “Development of New Wind Speed Maps for ASCE 7-16.” NIST Special Publication, In preparation. Mara, T.G. (2015). “Updated gust response factors for transmission line loading.” Proc. Electrical Transmission & Substation Structures Conference , ASCE, Branson, MO. Mara, T.G. and Behncke, R.H. (2015). “Examination of yawed wind loading on transmission structures.” Proc. Electrical Transmission & Substation Structures Conference , ASCE, Branson, MO. Mara, T.G. and Ho, T.C.E. (2011). “Design loads for transmission towers under skewed wind loading.” Proc. Structures Congress 2011, ASCE, Las Vegas, NV. Peterka, J. and Shahid, S. (1998). “Design gust wind speeds in the United States.” J. Struct. Eng ., 124(2), 207-214. Telecommunications Industry Association (TIA) (2005). Structural standard for antenna supporting structures and antennas. ANSI/TIA-222-G-2005, Arlington, VA.


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